Is the photon mass-less, or it's mass too small to measure

Have there been any experimental proof that light is mass-less?

Is it just too light to measure?

Well, the interesting question is: how you would tell the difference? All we know is that all the experimental data so far are consistent with a massless photon. Experiments only have a finite level of sensitivity, though, so tomorrow that could change.

In the meantime it is true to say that our best models of nature consider the photon to be massless, and we see no reason (yet) to alter those models for anything more complicated.